Solve for $x$ and $y$ using elimination. ${-3x+2y = 17}$ ${3x-5y = -47}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x+2y = 17}\thinspace$ to find $x$ ${-3x + 2}{(10)}{= 17}$ $-3x+20 = 17$ $-3x+20{-20} = 17{-20}$ $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ You can also plug ${y = 10}$ into $\thinspace {3x-5y = -47}\thinspace$ and get the same answer for $x$ : ${3x - 5}{(10)}{= -47}$ ${x = 1}$